Elliptic Curve Cryptography provides similar strength of protection comparing other public key cryptosystems but requires significantly smaller key size. This paper proposes a new faster scalar multiplication algorithm aiming at a more secured Elliptic Curve Cryptography scheme. This paper also proposes a novel Elliptic Curve Cryptography scheme where maximum length random sequence generation m...

Selection Algorithm and Generation Algorithm of elliptic curves have been the focus of research and hotspot of the Elliptic Curve Cryptosystem. This paper discusses a random elliptic curve realization method of Embedded Mobile Equipment, the SEA algorithm and its improved algorithm from Elliptic Curve's selection, Elliptic Curve's structure and Elliptic Curve's generation. Ensuring that the emb...

In this paper, we present algorithms for implementation of the GHS attack to Elliptic curve cryptosystems (ECC). In particular, we consider two large classes of elliptic curves over cubic extension fields of odd characteristics which have weak covering curves against GHS attack, whose existence have been shown recently [16][17][18]. We show an algorithm to find definition equation of the coveri...

This paper will examine the role of elliptic curves in the field of cryptography. The applicability of an analogous discrete logarithm problem to elliptic curve groups provides a basis for the security of elliptic curves. Two cryptographic protocols which implement elliptic curves are examined as well as two popular methods to solve the elliptic curve discrete logarithm problem. Finally, a comp...

This paper describes synthesizable VDHL implementation of elliptic curve Point Multiplication. Elliptic curves used for ECC are defined over mathematical structures called Galois fields. Based on the theory of ECC, this paper has carried out Modular addition/subtraction, EC Point doubling/addition, Modular multiplicative inversion, EC point multiplier, projective to affine coordinates conversio...

1. Introduction. If we wish to write the equations of curves of genus 1 that give elements of the Shafarevich-Tate group of an elliptic curve over a number field K, a choice of ways is open to us. For example, if the element in question is of order 3 the curve of genus 1 corresponding to it occurs as a smooth plane cubic curve over K. In a recent article [C-M] we raised the question of when one...

We survey elliptic curve implementations from several vantage points. We perform internet-wide scans for TLS on a large number of ports, as well as SSH and IPsec to measure elliptic curve support and implementation behaviors, and collect passive measurements of client curve support for TLS. We also perform active measurements to estimate server vulnerability to known attacks against elliptic cu...

Elliptic curve cryptography provides a methodology for obtaining high-speed, efficient, and scalable implementations of network security protocols. In this paper, we describe in detail three protocols based on elliptic curve cryptographic techniques, and the results of our implementation of the elliptic curve cryptography over the Galois field GF (2k), where k is a composite number. 1 Elliptic ...

We give a functorial construction of a rational S 1-equivariant cohomology theory from an elliptic curve equipped with suitable coordinate data. The elliptic curve may be recovered from the cohomology theory; indeed, the value of the cohomology theory on the compactification of an S 1-representation is given by the sheaf cohomology of a suitable line bundle on the curve. The construction is eas...